Hey guys!

I tried solving this problem from Atkins physical chemistry 8ed, exercise 2.6a (pg 71)

The problem goes like this:

A sample of 1.00 mol H_{2}O(g) is condensed isothermally and reversibly to liquid water at 100°C. The standard enthalpy of vaporisation of water at 100°C is 40.656kJmol^{-1}. Find w,q,ΔU and ΔH for this process.

Since it's given that the process is isothermal, I took ΔU to be zero and proceeded but the answer turned out to be something else(ΔU=-37.555kJmol^{-1} )I want to know why my assumption of taking ΔU=0 for an isothermal process is wrong here.